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An integral problem

  1. Dec 10, 2004 #1
    I have to solve this integral

    [tex]\int{\frac{x + 4a + b}{[x - (a + b)]^2 + c^2}}dx[/tex]

    where a, b, c are constant

    Could anybody know how to solve it ?
  2. jcsd
  3. Dec 11, 2004 #2


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    Homework Helper

    You can rewrite the integral as:

    [tex]\int{\frac{x - (a + b)}{[x - (a + b)]^2 + c^2}}dx + \int{\frac{5a+2b}{[x - (a + b)]^2 + c^2}}dx[/tex]

    Can you solve it now looking at the two integrals separately? Do you have integral tables to work with?
  4. Dec 11, 2004 #3


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    Homework Helper

    He doesn't need tables so solve this kind of integrals.Just well made substitutions.
    Your integral should be put in the form:
    [tex]\frac{1}{2}\int\frac{d[[x - (a + b)]^2+c^2]}{[x - (a + b)]^2 + c^2}+ (5a+2b)\int \frac{d[x-(a+b)]}{[x - (a + b)]^2 + c^2}[/tex]

    Do u see some patterns for substitutions which should bring the 2 integrals to familiar form??ln & artan in the final result??

  5. Dec 12, 2004 #4
    Thank you!
    I also came to get those result.
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